estimating extended supply -use tables in basic price s
TRANSCRIPT
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Estimating Extended Supply-Use Tables in Basic Prices with Firm
Heterogeneity for the United States:
A Proof of Concept
James J. Fetzer, Thomas F. Howells III, Lin Z. Jones, Erich H. Strassner, and Zhi Wang1
This paper presents proof-of-concept trade-in-value added (TiVA) statistics estimated from extended supply-use tables for the United States that account for firm heterogeneity. The tables used to estimate the TiVA statistics extend recently-introduced supply-use tables for the United States by disaggregating the components of supply and use by multinational and other firms. Recent research has shown both the advantages of measuring trade on a value added basis when analyzing bilateral trade flows and the dominance of multinational enterprises in U.S. trade in goods and services. Our TiVA statistics for the United States include measures based on traditional supply-use presentations as well as statistics that reflect firm-level heterogeneity for the year 2011. The comparative analysis of the two sets of statistics allows us to understand better how firms within industries engage in global value chains and if the incorporation of firm heterogeneity provides a more accurate measurement of TiVA. We find that domestic value added as a share of the value of exports is similar within large industry groups. However, there is much more variation in the value added share of exports when firm type is accounted for. Also, the additional granularity shows the share of this value added that comes directly from the producing industry varies much more across industries.
1 Fetzer, Howells, and Strassner are at the Bureau of Economic Analysis, U.S. Department of Commerce
([email protected], [email protected], and [email protected]). Jones is at the U.S. International Trade Commission ([email protected]) and Wang is at the Schar School of Policy and Government at George Mason University and the Research Center of Global Value Chains at the University of International Business and Economics in Beijing ([email protected]). We thank Paul Farello, Ray Mataloni, Sally Thompson, David Wassahusen, and Robert Yuskavage for helpful comments and conversations. We thank Christopher Wilderman for his assistance on the tax data and on concordances between classification systems. The views expressed in this paper are those of the author and should not be attributed to the Bureau of Economic Analysis, U.S. Department of Commerce or the U.S. International Trade Commission.
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1 Introduction
Pioneering work on measuring trade in value added (TiVA) began with efforts in
academia (e.g. Global Trade Analysis Project (GTAP)), in government (e.g. United States
International Trade Commission (USITC) and the World Input-Output Database (WIOD)), and in
international organizations (e.g. Organisation for Economic Co-operation (OECD) and World
Trade Organization). These initial efforts have raised the profile of TiVA and generated strong
demand for better understanding of how global value chains work, which has motivated
national statistical agencies to find ways to measure trade-in-value added (TiVA) more
accurately. Research has shown that a sizeable share of trade is composed of intermediate
goods that have crossed borders multiple times and that bilateral trade balances measured
using (TiVA) can be very different than the trade balances using gross trade flows (Johnson and
Noguera (2012)). These differences matter because they imply differences in competitiveness
vis-a-vis trading partners and their implications for trade policy.2
As noted by Fetzer and Strassner (2015) and others, national statistical agencies have
found direct measurement of TiVA to be impractical. Instead, efforts to measure TiVA more
accurately have focused on better refining supply-use tables (SUTs) that can be used to
measure the value added portion of trade indirectly by particular industries. Accurate
measurement of TiVA for a country using this method depends on the SUTs of all major trading
partners because the SUTs must be linked using bilateral trade flows. Improvements in these
2 See Dervis, Metzer and Foda (2013) “Value-Added Trade and Its Implications for Trade Policy”
http://www.brookings.edu/research/opinions/2013/04/02-implications-international-trade-policy-dervis-meltzer
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tables have benefitted from international collaboration on issues such as the industry and
product classifications and valuations of these tables. These efforts have also aimed to extend
these tables by taking into account different dimensions of firm-level heterogeneity within
industries and challenging the historical assumption of a homogenous production function for
all firms within a given industry.
This paper builds on recently-published SUTs for the United States (Young, Howells,
Strassner, and Wasshausen 2015). We estimate “proof of concept” extended SUTs
disaggregated by firm type based on the methodology of Fetzer and Strassner (2015). These
tables foreshadow more precise estimates of extended SUTs that will be the product of an
ongoing long-term U.S. Bureau of Economic Analysis (BEA) - U.S. Census Bureau (Census)
microdata link project. We also estimate measures of TiVA based on the input-output
coefficients derived from these SUTs.
2 Literature Review
Our paper builds on research that has decomposed industry output by firm type,
estimated extended input-output tables (IOTs), and estimated TiVA indicators using a single
country IOT. Recent research such as Fetzer and Strassner (2015), Piacentini and Fortanier
(2015), Ahmad, Araujo, Lo Turco, and Maggioni (2013), and Ma, Wang, and Zhu (2015) have
found evidence of heterogeneity in value added and trade between foreign- and domestic-
owned enterprises in a broad group of countries including the United States, China, and many
European countries. Our paper estimates the components of output and value added for
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multinational enterprises (MNEs) and non-MNEs for the United States based on the
methodology used in Fetzer and Strassner (2015).
We also build on the literature that uses firm characteristics and constrained
optimization to estimate IOTs by type of firm. Koopman, Wang, and Wei (2012) developed a
method that allows for computing IOTs that distinguish between processing and normal trade.
Ma, Wang, and Zhu (2015) extend this approach by distinguishing between Chinese exports by
foreign-invested enterprises and by Chinese-owned enterprises. We use this framework to
refine further the U.S. use table to include valuation at basic prices and to disaggregate the U.S.
SUT by firm type.
Most TiVA estimates are based on global IO tables, but it is possible to generate TiVA
estimates using a single country’s IO tables, under certain assumptions. Koopman, Wang, and
Wei (2014) indicate that gross exports can be decomposed into domestic content and foreign
content using a single country IOT if there is no trade in intermediate goods. Ma, Wang, and
Zhu (2015) note that single country models are limited to estimating the domestic content of
exports. The domestic content of exports may differ from the domestic value added in exports
since it may include domestic content that has been re-imported. Los, Timmer, and de Vries
(forthcoming) indicate that domestic value added in gross exports can be estimated from the
difference in reported gross domestic product (GDP) and hypothetical GDP estimated from a
single country IOT assuming the country does not export. However, they indicate that global
IOTs are required to decompose domestic value added by end use including the extent to which
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it is absorbed abroad. The weakness of this approach is that the U.S. production structure and
IOT would be different if the country did not export.
3 Data
The 2011 SUTs for the United States are the foundation on which the proof-of-concept
extended SUTs were constructed. The supply-use framework comprises two tables. The supply
table presents the total domestic supply of goods and services from both domestic and foreign
producers that are available for use in the domestic economy. The use table shows the use of
this supply by domestic industries as intermediate inputs and by final users as well as value
added by industry. The main part of each table is organized with industries across the columns
and commodities across the rows. The cells in the main part of the supply table indicate the
amount of each commodity (row) produced and/or used by an industry (column). The
remaining columns indicate the amount of each commodity that is imported and valuation
adjustments such as trade margins, transportation costs, taxes, and subsidies for each
commodity. The cells in the main part of the use table indicate the amount of a commodity
purchased as an intermediate input for an industry’s production process. The cells in the
remaining columns in the table indicate how each commodity is allocated to different
components of final demand. The cells in the bottom rows indicate how the components of
value added in an industry are allocated.3
3 Young, Howells, Strassner, and Wasshausen (2015).
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The incorporation of BEA statistics on the Activities of Multinational Enterprises (AMNE)
is how firm heterogeneity is introduced into the SUTs and is what distinguishes them as
extended SUTs. These statistics cover the financial and operating characteristics of U.S. parent
companies (domestic-owned MNEs) and U.S. affiliates that are majority-owned by foreign
MNEs (foreign-owned MNEs). They are based on legally mandatory surveys conducted by the
BEA and are used in a wide variety of studies, such as this one, to estimate the impact of MNEs
on the domestic (U.S.) economy and on foreign host economies.
The tables presented here are part of a time series of SUTs, now covering the period
1997-2014, that were first released by the BEA in September of 2015.4 Release of these tables
marks an important milestone in BEA’s long-term plan to make U.S. data on output,
intermediate inputs, and value added available in a format that is well suited for preparation of
TiVA statistics.
With the September 2015 release, data previously presented only in the make-use
format were also presented in the more internationally recognized supply-use format.5
Presentation in this format will facilitate future efforts to link U.S. data with SUTs from other
countries, a step necessary to derive the full suite of TiVA-related statistics. In addition, the new
SUTs incorporate important valuation changes that bring the tables into better alignment with
international standards and enhance the suitability of the tables for use in TiVA analysis. First,
taxes in the new tables are separated into taxes on products and other taxes on production and 4 For a full discussion of the supply-use framework and the methodology followed by BEA to prepare the
new tables, see Young, Howells, Strassner, and Wasshausen (2015). 5 The new supply and use tables are supplemental products that will be produced in addition to, rather
than in place of, BEA’s current make and use tables.
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output in the supply table, and value added in the use table is presented exclusive of taxes on
products (i.e. valued at basic prices). Second, a commodity distribution of customs duties on
imports is incorporated, and imports in the new tables are presented exclusive of duties (i.e.
valued at c.i.f.6).
Certain future enhancements to the SUTs are not reflected in the estimates presented
here. Currently, BEA is investigating the possibility of publishing tables on an International
Standard Industrial Classification (ISIC) basis. Additionally, BEA is investigating the possibility of
releasing a breakdown of the use tables valued at purchaser prices into their several
component matrices. This decomposition could include separate matrices for domestically-
produced inputs valued at basic prices, imported inputs at basic prices, margins, taxes on
products, and subsidies on products. These additions were not available for purposes of this
paper, so the tables were converted in a manner that approximates an ISIC basis and the
component matrices had to be estimated. The decomposition process is outlined in greater
detail in the methodology section and in appendix A.
The basic SUTs for 2011 are extended by incorporating data on firm-level heterogeneity
by industry. These data are prepared on an ISIC-basis for 33 industries following the
methodology used in Fetzer and Strassner (2015).7 As is the case in Fetzer and Strassner (2015),
we use 2011 IRS Statistics of Income (SOI) data to estimate value added by industry for all firms
with operations in the United States and BEA AMNE data for 2011. For U.S. MNEs, we 6 The c.i.f. valuation of imports refers to cost, insurance, and freight. This valuation includes the cost of
the import at the foreign port plus the insurance, freight charges, and charges other than import duties associated with transferring the import to the domestic port.
7 There is no BEA or IRS data for industry 34, “Private households with employed persons.”
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separately analyze data for domestic-owned MNEs and for foreign-owned MNEs. Because of
some challenges working directly with the SOI data, we also use data from the BEA input-
output accounts to estimate exports and intermediate imports. However, unlike Fetzer and
Strassner (2015) we use the enterprise level SOI data on employee compensation and make
adjustments to implausible values on a case-by-case basis. We also match these data on an
ISIC-basis for 33 ISIC industries from the reported NAICS industries. This industry conversion is
necessary so that our tables are comparable to those produced by other OECD countries.
Results by industry for domestic non-MNEs are computed as the difference between the
SOI-based results for all U.S. firms less the results for directly measured domestic-owned and
foreign-owned MNEs. We use the SOI data instead of the BEA SUTs because the SOI data are
collected and published by industry at the enterprise level, similar to the BEA AMNE data.
The data for foreign MNEs, which are U.S. affiliates of foreign parent companies, are
generally reported as published by BEA except where imports or exports are suppressed to
protect the confidentiality of firms that make up most of the data in the industry and where
gross operating surplus, consumption of fixed capital, and taxes were not published for an
industry. In these cases, we estimate the share for each of these variables for all industries for
which the data are not reported or are suppressed and then impute a value from this aggregate
share.
The data for domestic-owned MNEs are adjusted by removing the MNEs that are
majority-owned by foreign parents to put the data on an ultimate U.S.-owner basis, just as the
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foreign-owned MNE data are on an ultimate foreign-owner basis. Some industries had no
majority foreign-owned MNEs, so their data are the same as the regularly published data. We
impute data for several industries to protect the confidentiality of firms that make up a large
share of data for an industry. In these cases, we typically estimate the share of each variable
that needs to be imputed in the unadjusted data for all industries for which the data were not
reported or are suppressed and then impute a value from this aggregate share. One exception
is where we use unadjusted output shares to impute the imports and exports for industries
where the original unadjusted data were suppressed. Additionally, we reduce the trade data for
wholesale and retail trade for both domestic- and foreign-owned MNEs to better attribute the
trade to the using industries.8
We also make some adjustments to the SOI data to adjust for implausible values. Most
of the adjustments are made to employee compensation and to imports and exports, which in
total were based on the BEA SUTs. In particular we make large changes to values for
“Manufacturing not elsewhere classified and recycling.” The need to make large changes to
residual industry groups is typical because, by construction, these groups reflect measurement
error in all of the industry groups that are shown separately. There are no MNE data for public
administration and defense. We also assume that imports and exports were zero for public
administration and defense. Trade in both goods and services are included in the SOI data, but
only trade in goods is included in our MNE data. The BEA AMNE data include trade in services
and we are planning on incorporating this information along with information from our services
8 The adjustment is necessary because there is a wide body of evidence showing that wholesale
intermediaries play an important role in connecting imported products to using industries.
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surveys in the future. Therefore our tables may attribute a disproportionate share of trade in
services to domestic-owned non-MNEs.
4 Methodology
We take several steps to prepare the extended SUTs and to derive TiVA estimates from
both the standard and extended SUTs. As mentioned in the previous section, a decomposition
of the use table at purchasers’ prices into its several component matrices is not currently
available. Therefore, we first estimate this decomposition using a quadratic programming
constrained optimization model and data from the published BEA SUTs. We then estimate an
extended SUT in which industries are broken down into different firm types. Following the
approach taken by Ma, Wang, and Zhu (2015), this is also done using a quadratic programming
constrained optimization model with estimates of the components of output by firm type
derived from BEA and IRS data. We use the resulting extended SUTs to construct a symmetric
industry-by-industry extended input-output table (IOT). Using the IOT, we calculate the Leontief
inverse from which are derived our TiVA statistics.
4.1 Decomposing the purchasers’ price use table and constructing extended SUTs
and IOTs
The international standard is for use table transactions to be valued at purchaser prices.
However, a basic price valuation is preferred for purposes of calculating TiVA statistics because
it ensures more homogenous valuation across different products, more accurately reflects a
country’s input-output relationships, and allows separate identification of the effects of import
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tariffs, production taxes, and subsidies. Using a quadratic programming model with parameters
from BEA’s published SUTs, we decompose the purchaser price use table into separate matrices
for domestically-produced inputs valued at basic prices, imported inputs valued at basic prices,
margins, taxes on products, and subsidies on products. The model is detailed in Appendix A.
Following the decomposition of the purchaser price use table, we incorporate BEA and
IRS data on the components of output by firm type into the basic price SUT to construct
extended SUTs. We incorporate these data into the basic price SUT using an approach similar to
the constrained optimization model used by Ma, Wang, and Zhu (2015) for Chinese IOTs. We
estimate the share of output attributable to different types of firms: U.S.-owned MNEs, foreign-
owned MNEs, and non-MNEs. We then apply these shares to output of both primary and
secondary products and to taxes and margins in the supply tables to estimate the value of these
variables for each type of firm. Similarly, for the use table, we estimate the share of value
added attributable to each firm type from SOI and BEA data. We apply these shares to value
added in the use table. We then create a symmetric IOT from the SUTs for estimation of TiVA
statistics. The optimization model used for estimating extended SUTs is described in detail in
appendix B.
Tables 1 and 2 show a highly aggregated example of our proof-of-concept, extended
SUTs for the United States for 2011. Across the columns, the supply and use tables are arranged
first by the three firm-types: domestic-owned MNEs, foreign-owned MNEs, and domestic-
owned non-MNEs. The columns show an aggregation of industries of primary goods,
manufacturing, services, and unclassified “special” products. In this aggregation, the primary
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industry includes agriculture and mining while services include utilities, construction, other
private service industries and government services. The rows are arranged by firm types and
commodities, which are the same as those in the columns. Note that the rows and columns of
each table add up to total supply and total use of $29.5 trillion. This is composed of $2.1 trillion
in exports, $15.4 trillion of domestic final demand, and $12.0 trillion of total intermediate use.9
Tables 3 and 4 show the values in the aggregated SUTs as a share of total output. Table
3 shows that the largest shares in the supply tables are along the main diagonal. This indicates
that these highly aggregated groups of industries supply most of their output to firms in the
same industry. Also note that these shares do not vary much by firm type at this level of
aggregation. The table also shows that about two-thirds of imports are manufacturing
commodities.
According to table 4, all three types of firms generally purchase a higher share of their
output from domestic-owned non-MNEs than from MNEs. Also, table 4 indicates that
manufacturing imports are a larger share of output for MNEs compared with non-MNEs, but
imports of primary products are a larger share output for non-MNEs. Because trade in services
is not included for MNEs as noted earlier, non-MNEs are assigned a disproportionality large
share of trade in services.
9 An excel fi le of the extended tables for all 33 industries will be posted on the BEA website along with the
paper.
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4.2 TiVA estimates
Once the extended SUTs are constructed, we derive a symmetric industry-by-industry
extended IOT from the extended SUTs. First, we generate a commodity-by-commodity IOT
using the industry technology assumption that each industry has its own specific method of
production, irrespective of its product mix. We derive an industry-by-industry IOT using the
fixed product sales structure approach from this table, in which each product has its own
specific sales structure, irrespective of the industry in which it is produced.10 Dietzenbacher, Los,
Stehrer, Timmer, and de Vries (2013) note that this approach is also used to construct the world
IOTs for the World Input-Output Database Project. They indicate that practitioners prefer the
fixed product sales structure approach to the fixed industry sales structure where each industry
has its own sales structure. This is because it is more plausible that products have the same
sales structure than industries having the same sales structure. It also does not yield negative
values in cells that were not negative in the original SUT.
TiVA estimates are most rigorously calculated using international IOTs that account for
the production of all countries in the world. However, TiVA statistics can be calculated using
single country IOTs. We follow the approach of Ma, Wang, and Zhu (2015) and Tang, Wang, and
Wang (2014) and assume that domestic content in gross exports is the same as the value added
in exports. Because part of domestic content in gross exports is re-imported goods, domestic
content is an upper bound on domestic value added.
10 Eurostat (2008).
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We calculate TiVA measures using a methodology that is typically used for international
IOTs. A key to calculating TiVA statistics is the Leontief inverse of the IOT. The matrix depends
on both the direct input requirements from the same industry and the indirect input
requirements from other industries. Domestic value added embodied in gross exports for a
particular industry depends on both these direct and indirect requirements. Following Ma,
Wang, and Zhu (2015) and Tang, Wang, and Wang (2014), we calculate domestic value added as
the product of the vector of the domestic value added share of output for each industry, the
Leontief inverse of the U.S. IOT matrix, and the value of gross exports for each industry.
Likewise, the direct domestic value added content of gross exports is calculated as the vector of
domestic value added shares of output multiplied by the value of gross exports for each
industry. Indirect domestic content of gross exports is calculated as the difference between
total and direct domestic value added.
5 Results
In this section we describe the TiVA indicators from the U.S. IOTs. These TiVA indicators
help us better understand how an economy engages in global value chains. We find that the
domestic value added of exports is similar across large industry groups. However, there is much
more variation in the value added share of exports once firm type is considered. Also, the share
of this value added that comes directly from the producing industry varies much more across
industries than within industries.
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Powers (2012) points out that TiVA indicators typically focus on either a decomposition
of value added where goods are consumed or a decomposition of gross trade. He indicates that
examining trade on a value added basis shows a different picture of bilateral trade balances
than gross trade flows. However, the total trade deficit summed across all countries is identical
for both TiVA and gross trade flows.
One core measure of TiVA is decomposing value added of gross exports and imports into
domestic and foreign components. Other things being equal, the higher the foreign value added
share of exports, the more a particular industry is integrated in global value chains. This could
mean that the current level of exports depends on foreign content. It is also possible that the
foreign content is substituted for potential additional domestic content.
According to the OECD TiVA database, domestic value added as a share of exports for
the United States fluctuated slightly between 85 and 89 percent between 1997 and 2013. The
share is stable around 89 percent during 1997 to 2002 and then gradually decreases to 85
percent in 2008. Domestic value added embodied in gross exports fluctuates between 86 and
89 percent of gross exports during 2009 to 2013. The fluctuations during this period are most
likely due to the contraction of international trade following the financial crisis and the
subsequent recovery during that period.11
Domestic value added is a relatively larger share of exports for the United States
compared with other major economies. Domestic value added as a share of exports in 2011 for
the United States is similar to the share of domestic value added in exports for Australia, Japan, 11 OECD Trade in Value Added Database, Updated October 2015.
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and Russia, but about 10 percentage points higher than the share for most major European
countries and Canada, about 17 percentage points higher than the share for China and Mexico,
and about 27 percentage points higher than the share of domestic valued in exports for Korea.12
While this seems to suggest that the United States is relatively less integrated into global value
chains than many other major economies, it has the third highest level of foreign value added
content in exports in the world in 2011 at $286 billion. The only other countries with greater
foreign value added content of gross exports were China at $632 billion and Germany at $365
billion.
Before estimating TiVA statistics by firm type from the extended U.S. IOT, we calculate
TiVA statistics for all U.S. firms based on the 71 industry 2011 U.S. make and use tables.
Domestic value added as a share of gross exports for the United States varies by industry in
2011. As seen in figure 1, industries in the service sector generally have the highest shares of
domestic value added in their exports. Domestic value added as a share of exports for
industries in the services sector ranges from 77 percent to 99 percent. This is not surprising
given the labor intensive nature of services. One exception is the relatively more capital
intensive transportation services for which domestic value added as a share of exports is about
78 percent to 86 percent. Domestic value added as a share of output is slightly smaller for the
mining and extraction sector for which many inputs are geographically constrained to have a
domestic location compared to the services sector. Figure 2 shows that industries in the
manufacturing sector have more heterogeneity in the domestic value added as share of output,
12 “Domestic value added share of gross exports,” October 2015, OECD TiVA database.
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but in most cases the share is between 81 and 87 percent. A notable exception is petroleum and
coal products for which domestic value added makes up only slightly more than one half of the
value of exports. In 2011, the industry most likely used more imported foreign crude oil and
coal to produce refined petroleum and coal products for export.
Another core TiVA measure is to decompose the share of domestic value added in gross
exports into value added directly in the industry and indirect value added from other domestic
industries. This decomposition measures the degree to which an industry participates in a
domestic supply chain. Focusing on manufacturing industries in 2011, we see from figure 3 that
both direct and indirect domestic value added as a share of gross exports vary much more by
manufacturing industry than domestic value added as a share of gross exports.
The computer and electronic products industry has the largest share of direct domestic
value added in its gross exports. This reflects the industry’s high investment in R&D and its high-
skilled, high-paid labor force. The food, beverage, and tobacco industry has the largest share of
indirect domestic value added in its gross exports. This reflects the fact that its domestic value
added content mainly comes through intermediate inputs, particularly agricultural inputs.
Next we estimate TiVA statistics by firm type from our extended IOTs. Domestic value
added as share of exports does not vary much by type of firm on average, but the difference
varies between different types of firms for a particular industry. Table 5 shows that domestic
value added makes up 86 percent of gross exports for domestic-owned MNEs in 2011, similar to
the 88 percent share for non-MNEs, and the 80 percent share for foreign-owned MNEs.
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However, this share varies widely by industry, ranging from a minimum of 62 percent for coke,
petroleum products, and nuclear fuel to a maximum of 98 percent for renting of machinery and
equipment.
Table 6 shows that there are many instances of variability in domestic value added as a
share of output across different types of firms in the same industry. Domestic value added as a
share of output is smaller for foreign-owned MNEs compared with both domestic-owned MNEs
and domestic non-MNEs for all but a few industries. Although there are sizable differences
between domestic value added as a share of output for domestic-owned MNEs and non-MNEs
for many industries, there is no clear pattern for direction of those differences. The largest
differences are in agriculture and textiles.
Table 7 shows that although the average direct and indirect value added embodied in
gross exports is similar across firm type, there are differences by industry. The largest
differences are between MNEs and non-MNEs. For example, in the food products, beverage,
and tobacco industry, direct domestic value makes up more than 72 percent of the value of
gross exports while indirect domestic value makes up 69 percent of the value of gross exports
for non-MNEs. This suggests that the non-MNEs are much more integrated in domestic value
chains (including vertically integrated single firms) in these industries.
6 Conclusion
In this paper we construct proof-of-concept extended SUTs and TiVA estimates for the
United States. We do so by disaggregating production characteristics by type of firm and
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applying them to recently-introduced SUTs for the United States by the BEA (Young, Howells III,
Strassner and Wasshausen 2015). The project requires some modeling of basic price valuations
in order to translate BEA’s official use tables into domestic and import use, and to refine the
valuation of intermediate inputs and final demand from purchaser price valuation to basic
prices. This refinement to basic prices can be important for better understanding the economic
activity based on the theory of the firm. Basic price valuation removes taxation and trade policy
distortion from the estimates.
The results from this work build on a body of evidence found in other studies about the
importance of reflecting firm-level heterogeneity in traditional SUTs to understand global value
chains better through TiVA analysis. Our results indicate that heterogeneity by firm-type and by
ownership does matter particularly for industries such as agriculture, textiles, and construction.
Our analysis also reveals that it is a useful exercise to estimate TiVA from a single country SUT
and IOT. For example, the single-model approach does indeed allow for distinctions to be made
about how engaged domestic industries are in both global and domestic value chains, even if
there are some limitations in interpreting the indirect value added estimates. For example,
direct and indirect value added estimates reveal that the degree to which firms are integrated
in domestic production chains varies widely by industry.
Looking ahead, there are a suite of projects that remain on the agenda for the BEA and
for the USITC. These include collaborations with the OECD and with the Asia-Pacific Economic
Cooperation (APEC) where work continues to develop the framework for extended SUTs and to
develop APEC region SUTs and IOTs and associated TiVA estimates. The aim of this work is to
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incorporate the APEC database into the OECD database sometime around 2018. Additionally,
the BEA and the USITC are collaborating with Statistics Canada and the Instituto Nacional de
Estadistíca y Geografía to develop North America Regional SUTs and TiVA statistics with a goal
to complete the regional SUT and TiVA statistics in 2018 and extended tables and TiVA
measures around 2020.
Lastly, much work remains at the BEA to improve the economic infrastructure to
support global value chain efforts. This work includes enhancing the international comparability
of BEA’s SUTs and expanding the detail BEA publishes by type of service and by country. In
addition, a critical element is to produce official extended SUTs after completing a five-year
microdata linking project with the Census Bureau. This project will link BEA’s AMNE and trade in
services data with data from Census Bureau economic censuses and establishment surveys and
data on trade in goods. The output of this linking project will identify firm-level heterogeneity
tabulations that, ideally, will be made available for use on a recurring basis to construct official
statistics.
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Bernard, A. B., Jensen, J. B., & Schott, P.K. (2009). Importers, exporters, and multinationals. In Dunne, T., Jensen J. B., and Roberts, M. J. (Eds.), Producer dynamics: new evidence from micro data (pp. 513-551). Cambridge, MA: NBER, University of Chicago Press.
Curcuru, S. E. & Thomas, C. P. (2015). The return on U.S. direct investment at home and abroad. In Hulten, C. R. and Reinsdorf, M. B. (Eds.), Measuring wealth and financial intermediation and their links to the real economy (pp. 205-230). Cambridge, MA: NBER, University of Chicago Press. Dietzenbacher ,E., Los, B., Stehrer, R., Timmer, M.P., and de Vries, G.J. (2013). The Construction of World Input-Output Tables in the WIOD Project. Economic Systems Research, 25, 71-98. Fetzer, J.J. & Strassner, E.H. (2015). Identifying Heterogeneity in the Production Components of Globally Engaged Business Enterprises in the United States, BEA Working Paper WP2015-13. Johnson, Robert C. & Noguera, Guillermo (2012). Accounting for intermediates: production sharing and trade in value added. Journal of International Economics, 86(2), 224-236. Koopman, Wang, and Wei (2012). Tracing value-added and double counting in gross exports. American Economic Review, 104(2), 459-494. Los, B., Timmer, M.P. & de Vries, G.J. (Forthcoming). Tracing value-added and double counting in gross exports: comment. American Economic Review. Ma, H., Wang, Z., & Zhu, K. (2015). Domestic content in China’s exports and its distribution by firm ownership. Journal of Comparative Economics, 43(1), 3-18. Piacentini, M. & Fortanier, F. (2015). Firm heterogeneity and trade in value added. OECD Working Paper.
Samuels, J. D., Howells III, T. F., Russell, M., & Strassner, E. H. (2015). Import allocations across industries, import prices across countries, and estimates of industry growth and productivity. Houseman, S. N., & Mandel, M., (Eds.), Measuring globalization: better trade statistics for better policy (pp. 251-289.). Kalamazoo, MI: W.E. Upjohn Institute for Employment Research.
21
Tang, H., Wang, F., & Wang Z. (2014). The Domestic Segment of Global Supply Chains in China Under State Capitalism. World Bank Policy Research Paper 6960.
Young, J. A., Howells III, T. F., Strassner, E.H., & Wasshausen, D.B. (2015). BEA Briefing: Supply-Use Tables for the United States. Survey of Current Business 95:(9) , 1-8.
22
Table 1 Extended supply table at basic prices for United States, 2011 in millions of current US dollars
(Industries)
Domestic-owned MNE
Foreign-owned MNE
Domestic-owned non-MNE Imports Commodity
Supply
Primary Manuf Services
Primary Manuf Services
Primary Manuf Services
(Com
mod
ities
)
Dom
estic
M
NE Primary 102,770 177 186 103,134
Manufacturing 5,590 2,193,731 6,859 2,206,180 Services 3,015 106,170 3,320,068 3,429,252 Special products 0 1,446 119 1,564
Fore
ign
MNE
Primary
55,927 180 104
56,211 Manufacturing
3,246 936,219 3,000
942,465
Services
1,731 34,961 1,033,608
1,070,300 Special products
0 767 25
793
Non
-MNE
Primary 774,138 324 5,205 779,667 Manufacturing 22,072 2,430,895 29,104 2,482,071 Services 13,880 148,278 15,810,718 15,972,877 Special products 0 2,455 8,408 10,863
Impo
rts Primary
413,425 413,425
Manufacturing
1,649,390 1,649,390 Services
200,292 200,292
Special products
220,749 220,749
Total industry output 111,376 2,301,523 3,327,231 60,904 972,127 1,036,737 810,090 2,581,952 15,853,436 2,483,856 29,539,233
23
Table 2 Extended Use table at basic prices for United States, 2011 in millions of current US dollars
(Industries)
Domestic-owned MNE
Foreign-owned MNE
Domestic-owned non-MNE Domestic
Final Demand
Exports Total Use
Primary Manuf Services
Primary Manuf Services
Primary Manuf Services
(Com
mod
itie
s)
Dom
esti
c M
NE
Primary 513 21,207 1,222 275 8,450 703 6,761 26,324 8,839 22,675 6,165 103,134 Manufacturing 638 203,359 30,877 256 95,236 11,033 18,904 146,094 263,017 1,081,469 355,297 2,206,180 Services 2,603 97,343 404,804 1,306 40,544 136,712 43,721 116,771 1,050,261 1,398,120 137,066 3,429,252 Special products -85 141 -1,221 -46 279 -578 -993 266 -4,815 2,361 6,256 1,564
Fore
ign
MN
E Primary 283 10,977 701
158 4,518 406
3,228 14,168 5,005 12,246 4,521 56,211 Manufacturing 322 97,745 10,717
149 54,033 4,143
8,113 74,221 118,416 379,590 195,016 942,465
Services 844 35,336 105,008
431 14,475 36,888
14,978 40,774 303,854 430,306 87,406 1,070,300 Special products -43 72 -618
-23 141 -292
-503 134 -2,439 1,194 3,169 793
Non
-MN
E Primary 2,867 182,555 5,275 1,115 60,550 2,992 80,534 177,544 41,032 151,888 73,316 779,667 Manufacturing 982 217,581 53,128 402 106,008 19,048 26,531 255,685 465,087 945,656 391,964 2,482,071 Services 6,910 306,178 790,022 3,507 126,834 295,079 111,956 347,572 3,127,681 10,235,327 621,812 15,972,877 Special products -448 2,898 7,107 -243 2,088 384 -5,211 4,053 -3,436 -188,861 192,531 10,863
Impo
rts Primary 2,440 90,287 4,974
907 34,097 2,050
22,404 221,800 23,958 10,507
413,425
Manufacturing 9,803 190,217 100,796
6,484 165,206 80,839
12,154 140,758 127,268 815,864
1,649,390 Services 388 3,085 7,194
95 830 2,472
6,753 30,150 135,338 13,988
200,292
Special products 119 505 1,060
50 253 531
2,572 15,751 65,571 134,339
220,749
Total Intermediates 28,135 1,459,485 1,521,046 14,822 713,542 592,410 351,903 1,612,066 5,724,637 12,018,046
Value added 83,240 842,038 1,806,185 46,082 258,586 444,327 458,187 969,886 10,128,800
Total industry output 111,376 2,301,523 3,327,231 60,904 972,127 1,036,737 810,090 2,581,952 15,853,436 15,446,669 2,074,518 29,539,233
24
Table 3 Extended supply table at basic prices for United States, 2011, share of total output
(Industries)
Domestic-owned MNE
Foreign-owned MNE
Domestic-owned non-MNE Imports Commodity
Supply
Primary Manuf Services
Primary Manuf Services
Primary Manuf Services
(Com
mod
ities
)
Dom
estic
M
NE Primary 92 0 0 0
Manufacturing 5 95 0 7 Services 3 5 100 12 Special products 0 0 0 0
Fore
ign
MNE
Primary
92 0 0
0 Manufacturing
5 96 0
3
Services
3 4 100
4 Special products
0 0 0
0
Non
-MNE
Primary 96 0 0 3 Manufacturing 3 94 0 8 Services 2 6 100 54 Special products 0 0 0 0
Impo
rts Primary
17 1
Manufacturing
66 6 Services
8 1
Special products
9 1
Total industry output 100 100 100 100 100 100 100 100 100 100 100
25
Table 4 Extended use table at basic prices for United States, 2011, share of total output
(Industries)
Domestic-owned MNE
Foreign-owned MNE
Domestic-owned non-MNE Domestic Final
Demand Exports Total Use
Primary Manuf Services
Primary Manuf Services
Primary Manuf Services
(Com
mod
ities
)
Dom
estic
M
NE Primary 0 1 0 0 1 0 1 1 0 0 0 0
Manufacturing 1 9 1 0 10 1 2 6 2 7 17 7 Services 2 4 12 2 4 13 5 5 7 9 7 12 Special products 0 0 0 0 0 0 0 0 0 0 0 0
Fore
ign
MNE
Primary 0 0 0
0 0 0
0 1 0 0 0 0 Manufacturing 0 4 0
0 6 0
1 3 1 2 9 3
Services 1 2 3
1 1 4
2 2 2 3 4 4 Special products 0 0 0
0 0 0
0 0 0 0 0 0
Non
-MNE
Primary 3 8 0 2 6 0 10 7 0 1 4 3 Manufacturing 1 9 2 1 11 2 3 10 3 6 19 8 Services 6 13 24 6 13 28 14 13 20 66 30 54 Special products 0 0 0 0 0 0 -1 0 0 -1 9 0
Impo
rts Primary 2 4 0
1 4 0
3 9 0 0
1
Manufacturing 9 8 3
11 17 8
2 5 1 5
6 Services 0 0 0
0 0 0
1 1 1 0
1
Special products 0 0 0
0 0 0
0 1 0 1
1
Total Intermediates 25 63 46 24 73 57 43 62 36 41
Value added 75 37 54 76 27 43 57 38 64
Total industry output 100 100 100 100 100 100 100 100 100 100 100 100
26
Table 5 Domestic value added as a share of exports, by type of firm, by industry, 2011
ISIC Description Domestic
MNE Foreign
MNE Non-MNE
I01 Agriculture, hunting, forestry, and fishing 64 40 91 I02 Mining and quarrying 93 91 94 I03 Food products, beverages, and tobacco 92 89 86 I04 Textiles, textile products, leather, and footwear 76 58 90 I05 Wood and products of wood and cork 83 75 89 I06 Pulp, paper, paper products, printing, and publishing 91 78 93 I07 Coke refined petroleum products and nuclear fuel 62 57 47 I08 Chemicals and chemical products 90 87 92 I09 Rubber and plastics products 85 83 83 I10 Other non-metallic mineral products 85 90 86 I11 Basic metals 83 78 70 I12 Fabricated metal products except machinery and equip. 81 77 85 I13 Machinery and equipment n.e.c 83 77 81 I14 Computer electronic and optical products 93 82 91 I15 Electrical machinery and apparatus n.e.c 82 72 81 I16 Motor vehicles trailers and semi-trailers 81 76 73 I17 Other transport equipment 84 74 84 I18 Manufacturing n.e.c; recycling 92 83 80 I19 Electricity, gas, and water supply 93 88 93 I20 Construction 88 68 90 I21 Wholesale and retail trade; repairs 96 94 96 I22 Hotels and restaurants 93 89 94 I23 Transport and storage 91 83 81 I24 Post and telecommunications 93 87 91 I25 Finance and insurance 96 96 92 I26 Real estate activities 94 94 98 I27 Renting of machinery and equipment 97 88 95 I28 Computer and related activities 95 87 95 I29 Other business activities (incl. R&D) 95 90 96 I30 Public admin. and defence; compulsory social security 94 I31 Education 93 83 96 I32 Health and social work 88 69 96 I33 Other community, social, and personal services 91 78 95 All Industries 86 80 88 Minimum 62 40 47 Maximum 97 96 98
Note: The darker blue a cell is, the greater its value is from the “grand median” of all values in the table of 88. The darker red a cell is, the lesser its value is compared with 88.
27
Table 6 Differences in domestic value added as a share of exports, by type of firm, by industry, 2011
ISIC Description
Foreign MNE minus
Domestic MNE
Foreign MNE minus Non-MNE
Domestic MNE minus
Non-MNE
I01 Agriculture, hunting, forestry, and fishing -24 -51 -27 I02 Mining and quarrying -1 -2 -1 I03 Food products, beverages, and tobacco -2 4 6 I04 Textiles, textile products, leather, and footwear -18 -32 -14 I05 Wood and products of wood and cork -8 -13 -6 I06 Pulp, paper, paper products, printing, and publishing -14 -15 -2 I07 Coke refined petroleum products and nuclear fuel -5 10 15 I08 Chemicals and chemical products -3 -5 -2 I09 Rubber and plastics products -3 0 3 I10 Other non-metallic mineral products 5 4 -1 I11 Basic metals -4 8 13 I12 Fabricated metal products except machinery and equip. -4 -8 -3 I13 Machinery and equipment n.e.c -5 -4 2 I14 Computer electronic and optical products -11 -9 2 I15 Electrical machinery and apparatus n.e.c -9 -8 1 I16 Motor vehicles trailers and semi-trailers -5 3 8 I17 Other transport equipment -11 -11 0 I18 Manufacturing n.e.c; recycling -9 3 12 I19 Electricity, gas, and water supply -5 -5 0 I20 Construction -20 -22 -2 I21 Wholesale and retail trade; repairs -3 -3 0 I22 Hotels and restaurants -4 -5 -1 I23 Transport and storage -8 2 10 I24 Post and telecommunications -6 -4 2 I25 Finance and insurance 0 3 4 I26 Real estate activities 1 -4 -5 I27 Renting of machinery and equipment -8 -7 1 I28 Computer and related activities -8 -8 0 I29 Other business activities (incl. R&D) -5 -5 -1 I30 Public admin. and defence; compulsory social security
I31 Education -10 -13 -3 I32 Health and social work -19 -27 -9 I33 Other community, social, and personal services -12 -17 -4
Note: Blue cells indicate negative values and yellow cells indicate positive values.
28
Table 7 Direct and indirect domestic value added as a share of gross output, by type of firm, by industry, 2011
ISIC Description Direct Indirect Dom. MNE
For. MNE
Non- MNE
Dom. MNE
For. MNE
Non- MNE
I01 Agriculture, hunting, forestry, and fishing 15 19 54 49 21 37 I02 Mining and quarrying 30 36 17 62 56 77 I03 Food products, beverages, and tobacco 78 72 16 13 17 69 I04 Textiles, textile products, leather, and footwear 51 33 69 25 25 20 I05 Wood and products of wood and cork 21 35 36 63 40 53 I06 Pulp, paper, paper products, printing, and publishing 42 40 68 50 37 25 I07 Coke refined petroleum products and nuclear fuel 46 48 21 16 9 26 I08 Chemicals and chemical products 61 58 48 29 29 44 I09 Rubber and plastics products 28 42 53 57 40 30 I10 Other non-metallic mineral products 51 36 53 34 54 33 I11 Basic metals 28 24 23 54 54 47 I12 Fabricated metal products except machinery and
equipment 34 35 35 48 42 50
I13 Machinery and equipment n.e.c 74 67 73 9 11 8 I14 Computer electronic and optical products 80 76 70 13 7 21 I15 Electrical machinery and apparatus n.e.c 74 66 52 8 6 29 I16 Motor vehicles trailers and semi-trailers 42 59 70 39 17 3 I17 Other transport equipment 59 67 84 25 7 1 I18 Manufacturing n.e.c; recycling 88 81 78 4 2 2 I19 Electricity, gas, and water supply 18 6 2 74 82 91 I20 Construction 32 5 0 56 63 90 I21 Wholesale and retail trade; repairs 42 54 16 55 39 80 I22 Hotels and restaurants 14 6 16 79 83 78 I23 Transport and storage 1 3 58 91 80 23 I24 Post and telecommunications 27 25 41 66 63 50 I25 Finance and insurance 1 0 71 95 95 22 I26 Real estate activities 0 0 7 93 94 91 I27 Renting of machinery and equipment 6 3 70 91 85 25 I28 Computer and related activities 58 14 44 37 73 52 I29 Other business activities (incl. R&D) 4 3 16 91 87 80 I30 Public admin. and defence; compulsory social security 0 0 85 0 0 9 I31 Education 37 20 51 56 62 45 I32 Health and social work 27 63 52 60 7 45 I33 Other community, social, and personal services 26 29 59 64 50 36 All Industries 47 47 49 39 33 39 Note: The darker blue a cell is, the greater its value is from the “grand median” of all values in the table of 38. The darker red a cell is, the lesser its value compared with 38.
29
Figure 1 Domestic value added as a share of gross exports by industry, 2011
0
20
40
60
80
100
Shar
e of
gros
s exp
orts
Transportation Services
Services Manufacturing Mining/ Extraction
All industry average share= 86 percent
Farms/ Forestry/ Fishing
Utilities/ Construction
30
Figure 2 Domestic value added as a share of gross exports by manufacturing industry, 2011
87 88
72
83 79
8980
7181 82
87 85 8187
8188
54
8580
0
20
40
60
80
100
Shar
e of
gros
s exp
orts
31
Figure 3 Direct and indirect domestic value added (DVA) as a share of gross exports by manufacturing industry, 2011
31 3820
38 36
64
3922
44 3648
25 2839
3046
2141
32
56 50
52
45 44
25
40
49
37 4639
60 5348
51
42
33
4448
0
20
40
60
80
100
Shar
e of
gros
s exp
orts
Direct DVA Indirect DVA
32
Appendix A: Refining the use table valued at basic prices
To develop separate matrices for domestically-produced inputs valued at basic prices,
imported inputs at basic prices, margins, taxes on products, and subsidies on products, we solve
a quadratic programming model with parameters from BEA’s published SUTs. Before
introducing the estimation model, let us review the major data reported in the BEA Supply-Use
IO tables. At the product and sector level (73 groups of products and 71 industries), we know
the following values from the supply table:
cjtx0 = Output of product group c by industry j at year t, basic prices, 73 by 71 matrix;
ctm0 = Imports from the world of product group c at year t, cif prices, 73 by 1 vector;
ctTSb0 = Total supply of product c at year t, basic prices;
ctTmg0 = Total trade margins by product c at year t, 73 by 1 vector;
ctTtrs0 = Total transport margins by product c at year t, 73 by 1 vector; itxctTtxc0 = Total tax by product c at year t, (import duty, Tax and Subsidies) 73 by 3
matrix
ctTSp0 = Total supply of product c at year t, purchaser prices, 71 by 1 vector; We also know following values from the use tables:
citzp0 = Product c used by industry i at year t, purchaser prices, 73 by 71 matrix
itvb0 = total value added of industry i at basic prices at year t, 1 by 71 vector
itTXIb0 = Total output of industry i at year t, basic prices, 1 by 71 vector itxitTtxi0 = Total tax/duty or subsidy by industry i at year t, (tax and import duties,
subsidies 2 by 71 matrix)
chtyp0 = Product c used by final user h at year t, purchaser prices
cte0 = Exports to the world of product group c at year t, fob prices
ctTUp0 = Total use of product group c at year t, purchaser prices; From the import use tables we know these values:
citzmb0 = Imported product c used by industry i at year t, basic prices
33
chtymb0 = Imported product c used by final user h at year t, basic prices These data will be used as parameters (right hand constant) to construct the linear
constraints and the initial value of variables in the estimation model.
Model specification: The notation used to specify the programming model is as follows: Index: I ={ 01…71}; C ={ 01…73}; H = { F01,F02,IVT ,GOV, EXP} NMG ={ 1…26,36,38…73}; MGC ={ 27…35,37};ITX={TAX,DUTY,SUB} Variables (Unknowns: basic-price-based intermediate transactions and final demand
transactions) :
citzb = Product c used by industry i at year t, basic prices
chtyb = Product c used by final user h at year t, basic prices
citzdb = Domestic made product c used by industry i at year t, basic prices
chtydb = Domestic made product c used by final user h at year t, basic prices The following variables constitute the valuation matrix. Each margin has the same
dimension as the corresponding use table: mgccitmgi = Trade and transport margins for intermediate input of Product c used by
industry i at year t (10 by 73 by 71 array); mgccitmgy = Trade and transport margins for final use of Product c used by final user h at
year t (10 by 73 by 5 array) itxcitntxi = tax for intermediate input of Product c used by industry i at year t (3 by 73 by
71 array); itxchtntxy = tax for final use of Product c used by final user h at year t (3 by 73 by 71 array);
The estimation model is based on the economic and statistical relationship between
elements in the use table valued at basic prices and elements in the use table valued at
purchaser prices. These are used to construct several linear equations as constraints and to
compute the initial values of variables that are used to formulate an optimization problem to
minimize the deviation of the solution values from the initial values of these variables.
34
Constraints: The relationship between cells of the use table based on basic prices and the use table
based on purchaser prices is:
For non-margin products: C = NMG
cititx
itx
mgc
mgccitcit zpnetimgizb
cit0
3
1
10
1=++ ∑∑
==
(A.1)
chtitx
itx
mgc
mgcchtcht ypntxymgyyb
cht0
3
1
10
1=++ ∑∑
==
(A.2)
For margin products: C=MGC
cititx
itx
nmg
mgccitcit zpnetimgizb
cit0
3
1
73
=+− ∑∑=
(A.3)
chtitx
itx
nmg
mgcchtcht ypntxymgyyb
cht0
3
1
73
=+− ∑∑=
(A.4)
The split between domestic and import use at basic prices is assumed to be:
citcitcit zbzmzd =+ 0 (A.5)
chtchtcht ybymyd =+ 0 (A.6) Basic balance condition Supply and use balance for each product groups at purchaser prices: For non-margin products: C=NMG
cth itx
itx
mgc
mgcchtcht
i itx
itx
mgc
mgccitcit TSpntxymgyybnetimgizb
chtcit0)()(
5
1
3
1
10
1
71
1
3
1
10
1=+++++ ∑ ∑∑∑ ∑∑
= === ==
(A.7)
For margin products: C=MGC
cth itx
itx
nmg
mgcchtcht
i itx
itx
nmg
mgccitcit TSpntxymgyybnetimgizb
chtcit0)()(
5
1
3
1
7371
1
3
1
73
=+−++− ∑ ∑∑∑ ∑∑= == =
(A.8)
Supply and use balance for each product group at basic prices:
35
0 0071
1
5
1
71
1ct
ictcit
hcht
subtax
icit TSbmxybnetinetizb
citcit=+=+++ ∑∑∑
===
for all c (A.9)
Input cost and total output balance for each industry at basic prices:
itc
ictl
iftsubtax
citcit1=c
TXIbxvbnetinetizmzd citcit
000)0(73
1
3
1
73
∑∑∑==
==++++ for all i (A.10)
Balance condition for total domestic product output and use at basic prices:
∑∑∑=
=+++71
1
671
0i
ictsubtax
cht=1h
cit=1i
xnetinetiydzd citcit
for all c (A.11)
Balance condition for total import supply and use at basic prices:
ctcht=1h
cit=1i
mymzm 0771
=+∑∑ for all c (A.12)
Transportation cost, trade margins and net tax constraints Trade and transport margin supply and use balance: For MGC={27…31}
ctnmgc i
mgccht
mgccit Tmgmgymgi 0)(
73 71
1−=+∑ ∑
= =
(A.13)
For MGC ={32…35,37}
ctnmgc i
mgccht
mgccit Ttrsmgymgi 0)(
73 71
1−=+∑ ∑
= =
(A.14)
Domestic trade and transportation cost constraints for non-margin products: For C=NMG and MGC={27…31}
ctmgc h
mgccht
mgc i
mgccit Tmgmgymgi 0
5
1
71
1=+∑∑∑∑
==
(A.15)
For C=NMG and MGC={32…35,37}
ctmgc h
mgccht
mgc i
mgccit Ttrsmgymgi 0
5
1
71
1=+∑∑∑∑
==
(A.16)
Tax constraints for each product group:
itxct
h
itxcht
i
itx Ttxcntxyntxicit
05
1
71
1=+∑∑
==
for all c (A.17)
Tax and duty constraints for each industry:
36
itxit
c
itx Ttxintxicit
073
1=∑
=
for all i (A.18)
Aggregate expenditure components constraints:
htitx
itxcht
nmg mgc
mgccht
hcht
c
GDPEntxymgyyb =++ ∑∑ ∑∑∑===
)(3
1
73 10
1
473
1 for all h except EXP (A.19)
GDP from the production side:
ti c itx
itxcit
fift GDPntxivb∑ ∑∑∑
= = ==
=+71
1
73
1
3
1
3
1) (A.20)
GDP from the expenditure side:
tc
ctcth
ht GDPmeGDPE =−+∑∑==
])00(73
1
5
1 (A.21)
The objective function:
−
++
+++
+−
+−
∑∑∑∑∑∑
∑∑∑∑ ∑∑∑∑
∑∑∑∑∑∑
== =
−
=
−
== = =
−
=
−
=
−
= == =
ntxi
ntxintxi ntxy
ntxyntxy
mgy
mgymgy
mgimgimgi
ymymym
ydydyd
zmzmzm
zdzdzd
citxcit
itxcit
itxcit
1=itx1=ih itxitxcht
itxcht
itxcht
=c
h
mgccht
mgccht
mgccht
c=mgcmgc i cmgccit
mgccit
mgccit
h cht
chtcht
=c
h cht
chtcht
=cc i cit
citcit
c i cit
citcit
73
1
23716
1
3
1
2(
73
1
6
1
2(
73
1
10
1
10
1
71
1
73
1
2(6
1
2(
73
1
6
1
2(
71
1
73
1
71
1
273
1
71
1
2
0)0(
0)0
0)0
0)0
0)0
0)0)0(
0)0(
21= SMin
To obtain a solution the problem, we minimize the objective function subject to
constraints (A.1) to (A.21).
Initial values for all unknowns in the constrained optimization problem are based on
various proportionality assumptions and other BEA data. Notice that the initial values obtained
usually do not satisfy the linear constraints.
Variable initiation:
ct
itxctitx
ct TSbTtxc
=τ (tax rate computed from supply table)
37
itxcitntxi0 = itx
ctτ citprz _ net tax rate multiplied by industry cells at producer prices from the traditional use table;
itxchtntxy0 = cht
itxct pry _τ net tax rate multiplied by final demand by categories at
producer prices from the traditional use tables
citzmb0 = industry cells from the import use table before redefinition
chtymb0 = final demand by categories from the import use table before redefinition
citzdb0 = ∑=
−−3
100_
itxcitcitcit ntxizmbprz
chtydb0 = ∑=
−−3
100_
itxchtcitcit ntxyymbpry
citzb0 = ∑=
−3
10_
itxcitcit ntxiprz
chtyb0 = ∑=
−3
10_
itxchtcit ntxypry
Using the 2007 margin table, we compute a transportation cost rate and apply it to 1997 and 2011
cit
citcit zp
mgimrt = , t=2007
citmgi0 = citcit zpmrt
chtmgy0 = total trade margin in PCE and PQE bridge table Trade margin products
42 Wholesale trade C27 441 Motor vehicle and parts dealers C28 445 Food and beverage stores C29 452 General merchandise stores C30 4A0 Other retail C31
Transportation margin products
81 Air transportation C32
82 Rail transportation C33
83 Water transportation C34 Truck transportation C35
39
Appendix B: Estimating extended supply and use tables at basic prices
Statistical agencies in most countries do not currently disaggregate standard supply and
use tables (SUTs) into extended SUTs by firm type. Thus, we develop a method to construct
those subaccounts based on the original SUT. The SUTs already include data on industry-level
output, value added, imports, exports, and aggregate inter-industry transactions. To estimate
the extended SUT with firm type sub-accounts, we need to complement the official statistics
with aggregated micro-level data.
Data required:
Supply and use tables in both basic and purchaser prices, the import use table at cif
prices, aggregated micro data gross output, value added, exports and imports, by firm type
The notation used to specify the estimation model is as follows:
Index: F={MNE_D,MNE_F,OTH} I ={ 01…33}; C ={ 01…35}; H = { HC,GCF,IVT,GOV, EXP} NMG ={0 1…,20,22,24…35}; MGC ={ 21,23};ITX={TAX,DUTY,SUB} Parameters known from standard supply and use tables
ctTXCb0 = Total output of product group c at year t, basic prices
itTXIb0 = Total output of industry i at year t, basic prices
citzp0 = Product c used by industry i at year t, purchaser prices
citzdb0 = Domestic product c used by industry i at year t, basic prices
citzmb0 = Imported product c used by industry i at year t, basic prices
ctyd0 = Domestic product c used by domestic final user at year t, basic prices
ctym0 = Imported product c used by domestic final user at year t, basic prices
40
cjt0sup = Output of product group c by industry j at year t, basic prices
itvb0 = Total value added of industry i at basic prices at year t,
chtyp0 = Product c used by final user h at year t, purchaser prices
ctex0 = Exports to the world of product group c at year t, fob prices
ctmx0 = Imports from the world of product group c at year t, cif prices itxitTtxi0 = Total tax by industries at year t, itxctTtxc0 = Total tax by products at year t,
ctTmg0 = Total trade margins by Product at year t
ctTtrs0 = Total transport margins by Product at year t
htGDPE0 = Gross domestic product (GDP) by major expenditure category
tGDP0 = Gross domestic product (GDP) Variables will be estimated by the model:
fsfcitzd = Domestic made product c used by industry i between firm type fs (supplying
firm) and f (using firm) at year t, basic prices f
ctyd = Domestic made product c by firm f used by domestic final user at year t, basic prices
fcitzm = Imported product c used by firm f in industry i at year t, basic prices
fcitx = Output of product group c by firm type f of industry i at year t, basic prices f
itv = Total value added of firm type f in industry i at basic prices at year t,
fcte = Exports to the world of product group c by firm type f at year t, fob prices
fsfmgccitmgi , = Trade and transport margins for intermediate input of Product c used by
industry i at year t between firm type fs (supplying firm) and f (using firm) fmgc
ctmgy , = Trade and transport margins for final use of product c used by domestic final user and exporter at year t of firm type f
fsfitxcittxi , = Tax for intermediate input of product c used by industry i at year t between
firm type fs (supplying firm) and f (using firm) fitx
cttxy , = Tax for final use of product c used by domestic final user and exporter at year t of firm type f
Variable initiation:
41
∑=
= 3
1f
fit
fitf
i
go
goXsh where f
itgo is gross output by firm type f from micro data
∑=
= 3
1f
fit
fitf
i
V
VVsh where f
itv is value added in industry i by firm type f from micro data
∑=
= 3
1f
fct
fctf
c
m
mMsh where f
ctm is imports of product c by firm type f from micro data
∑=
= 3
1f
fct
fctf
c
e
eEsh where f
cte is exports of product c by firm type f from micro data
ctf
cfct exEshe 00 ×=
ctf
cfct VbVshv 00 ×=
citf
ifcit Xshx 0sup0 ×=
fit
c
fict
fit vxInt 00
35
1−= ∑
=
where fitv is value added by firm type f from micro data
∑=
= 3
1f
fit
fitf
it
Int
IntIntsh
cjtfj
fi
ffcjt zdbIntshxshzd 00 2121 ××=
cjtfj
fc
fcjt zmbIntshmshzm 00 ××=
∑∑∑==
−−=3
12
332
33
1000
f
fct
i
ffcit
i
fcit
fct ezdxyd
Model specification: Constraints: (to simplify the estimation model we aggregate the five categories of final
demand into domestic final demand and exports) Basic balance condition Supply and use balance for each product groups at purchaser prices For non-margin products: C=NMG all f
42
ctf itx
fitxct
f mgc
fmgcct
fct
fct
fct
i fs f itx
fsfitx
mgc fs f
fsfmgccit
f
fcit
fs f
fsfcit
TSptxymgyymeyd
tximgizmzdcit
0)0)(3
1
3
1
,3
1
2
1
,3
1
33
1
3
1
3
1
3
1
,2
1
3
1
3
1
,3
1
3
1
3
1
=+++++
+++
∑∑∑ ∑∑
∑ ∑∑∑∑ ∑∑∑∑∑
= == ==
= = = == = === = (B.1)
For margin products: C=MGC, all f
ctf itx
fitxct
f mgc
fmgcct
f
fct
fct
fct
i fs f itx
fsfitx
nmg fs f
fsfmgccit
f
fcit
fs f
fsfcit
TSptxymgyymeyd
tximgizmzdcit
0)(3
1
3
1
,3
1
2
1
,3
1
33
1
3
1
3
1
3
1
,35
1
3
1
3
1
,3
1
3
1
3
1
=+−+++
+−+
∑∑∑ ∑∑
∑ ∑∑∑∑ ∑∑∑∑∑
= == ==
= = = == = === = (B.2)
Input cost and total output balance for each industry at basic prices, for all i and f
∑∑∑∑∑∑∑== == ==
=++++35
1
35
1
3
1
,35
1
3
1
,3
1
35
)(c
fict
fit
c s
fsfsubcit
c s
fsftaxcit
f
fcit
fsfcit
1=c
xvtxitxizmzd (B.3)
Balance condition for total domestic product output and use at basic prices, for all c and
all f
∑∑∑∑∑∑===
=++++33
1
35""
35 33
1
""3
1
33
i
fict
nmg
subcit
nmg i
taxcit
fct
fct
fs
fsfcit
=1i
xtxitxieydzd (B.4)
Balance condition for total import supply and use at basic prices for all c:
ctctf
fcit
=1i
mxymzm 003
1
33
=+∑∑=
(B.5)
Transportation cost, trade margins and net tax constraints Trade and transport margin supply and use balance For MGC={21}
ctnmgc i f fs
fmgcct
fsfmgccit Tmgmgymgi 0)(
35 33
1
3
1
3
1
,, −=+∑ ∑∑ ∑= = = =
(B.6)
For MGC ={23}
ctnmgc i f fs
fmgcct
fsfmgccit Ttrsmgymgi 0)(
35 33
1
3
1
3
1
,, −=+∑ ∑∑ ∑= = = =
(B.7)
Domestic trade and transportation cost constraints for non-margin products For C=NMG and MGC={21}
43
ctmgc f
fmgcct
mgc i fs f
fsfmgccit Tmgmgymgi 0
3
1
,33
1
3
1
3, =+∑∑∑∑∑∑
== =
(B.8)
For C=NMG and MGC={23}
ctmgc
mgcct
mgc i
mgccit Ttrsmgymgi 0
33
1=+∑∑∑
=
(B.9)
Tax constraints for each product group, for all c
itxct
f
fitxct
i fs f
fsfitx Ttxctxytxicit
03
1
,33
1
3
1
3
1
, =+∑∑∑∑== = =
(B.10)
Tax and duty constraints for each industry for all i
itxit
fs f c
fsfitx Ttxitxicit
03
1
3
1
35
1
, =∑∑∑= = =
(B.11)
GDP constraints:
tf itx
fitxct
nmg f mgc
fmgcctct
f
fct
fct
c
GDPtxymgymeyd =++−+ ∑∑∑∑ ∑∑∑= == ===
))0)((3
1
3
1
,35 3
1
2
1
,3
1
35
1 (B.12)
Adding up constraints: Relationship between use table cells based on basic prices and purchaser prices: For non-margin products: C = NMG
citfs f itx
fsfixcit
fs f mgc
fsfmgccit
f
fcit
fs f
fsfcit zptximgizmzd 0
3
1
3
1
3
1
,3
1
3
1
2
1
,3
1
3
1
3
1=+++ ∑∑∑∑∑ ∑∑∑∑
= = == = === =
(B.13)
∑∑∑∑ ∑∑== == ==
=++++5
1
3
1
3
1
,2
1
3
1
,3
100)(
hcht
f itx
fitxct
mgc f
fmgcct
fct
fct
fct yptxymgyymeyd (B.14)
For margin products: C=MGC
citfs f itx
fsfixcit
fs f mgc
fsfmgccit
f
fcit
fs f
fsfcit zptximgizmzd 0
3
1
3
1
3
1
,3
1
3
1
2
1
,3
12
3
1
3
1=+−+ ∑∑∑∑∑ ∑∑∑∑
= = == = === =
(B.15)
∑∑∑∑ ∑∑== == ==
=+−++5
1
3
1
3
1
,2
1
3
1
,3
10)(
hcht
f itx
fitxct
mgc f
fmgcct
fct
fct
fct yptxymgyymeyd (B.16)
cjtf
fcitx 0sup
3
1=∑
= (B.17)
44
Or cti f
fcit TXPbx 0
33
1
3
1=∑∑
= =
and ctc f
fcit TXIbx 0
35
1
3
1=∑∑
= =
ctf
fct exe 0
3
1=∑
=
; for all c (B.18)
itf
fit vbv 0
3
1=∑
=
for all i (B.19)
The objective function:
+
−++
+++
+−
+−
∑∑∑
∑ ∑∑∑∑∑∑∑
∑ ∑∑∑∑∑∑∑∑
∑∑∑∑∑∑∑∑∑
=
−
=
= = == =
−
= = = = =
−
=
−
=
−
=
−
= = == = = =
txy
txytxy
txitxitxi
mgymgymgy
mgi
mgimgie
ee
vvv
ydydyd
zm
zmzm
zdzdzd
ffitx
ct
fitxct
fitxct
itx=c
c fs ffsfitx
cit
fsfitxcit
fsfitxcit
=1itx=1ic ffmgc
ct
fmgcct
fmgcct
=mgc
mgc i c fs ffsfmgc
cit
fsfmgccit
fsfmgccit
ffct
fit
fct
=cffit
fit
fit
=i
ffct
fct
fct
=cc i ffcit
fcit
fcit
c i f ftfftcit
fftcit
fftcit
3
1,
2,,(3
1
35
1
35
1
3
1
3
1,
2,,33335
1
3
1,
2,,(2
1
2
1
33
1
35
1
3
1
3
1,
2,,(3
1
2(35
1
3
1
2(33
1
3
1
2(35
1
35
1
33
1
3
1
235
1
33
1
3
1
3
1
2
0)0
0)0(
0)0
0)0
0)0
0)0
0)0
0)0(
0)0(
21= SMin
(B.20)
Scheme of Extended Use Table Intermediate use Final
use Exports Domestic
or Imported supply
MNE_D MNE_F OTH
Domestic Intermediate use
MNE_D DtoDZ DtoFZ DtoOZ DY DE DX MNE_F FtoDZ FtoFZ FtoOZ FY FE FX OTH OtoDZ OtoFZ OtoOZ OY OE OX
Imports MtoDZ MtoFZ MtoOZ MY
Value added DV FV OV Gross Input TDX )( TFX )( TOX )(
M